We have studied the random-axis magnet with infinite anisotropy by three methods: Cayley-tree approximation, Migdal-Kadanoff renormalization group (MKRG), and Imry-Ma scaling. In the Cayley-tree approximation, by an examination of susceptibilities, it is shown that there exists a competition between the coordination number z and the number of components n of the spins which leads to either ferromagnetic or spin-glass order. Using the MKRG at very low temperature we map out approximately the regimes of the ferromagnetic, spin-glass, and disordered phases as a function of n and the spatial dimension, d. The Imry-Ma arguments are made as an additional method for obtaining information on the critical dimension. Comparisons of these results with the previous literature are made.We have studied the random-axis magnet with infinite anisotropy by three methods: Cayley-tree approximation, Migdal-Kadanoff renormalization group (MKRG), and Imry-Ma scaling. In the Cayley-tree approximation, by an examination of susceptibilities, it is shown that there exists a competition between the coordination number z and the number of components n of the spins which leads to either ferromagnetic or spin-glass order. Using the MKRG at very low temperature we map out approximately the regimes of the ferromagnetic, spin-glass, and disordered phases as a function of n and the spatial dimension, d. The Imry-Ma arguments are made as an additional method for obtaining information on the critical dimension. Comparisons of these results with the previous literature are made.

Physical review. B, Condensed matterApr 1, 198722 citations

Transverse Ising spin-glass model

Raimundo R. dos Santos, Rita Zorzenon dos Santos, Mauricio Kischinhevsky

We discuss the zero-temperature behavior of the transverse Ising spin-glass ($\ifmmode\pm\else\textpm\fi{}{J}_{0}$) model. The $d$ -dimensional quantum model is shown to be equivalent to a classical ( $d+1$ )-dimensional Ising spin glass with correlated disorder. A renormalization-group treatment of the one-dimensional quantum model indicates the existence of a spin-glass phase. The Migdal-Kadanoff approximation is used to obtain the phase diagram of the quantum spin glass in two dimensions.We discuss the zero-temperature behavior of the transverse Ising spin-glass ($\ifmmode\pm\else\textpm\fi{}{J}_{0}$) model. The $d$-dimensional quantum model is shown to be equivalent to a classical ($d+1$)-dimensional Ising spin glass with correlated disorder. A renormalization-group treatment of the one-dimensional quantum model indicates the existence of a spin-glass phase. The Migdal-Kadanoff approximation is used to obtain the phase diagram of the quantum spin glass in two dimensions.

Physical review. B, Condensed matterApr 1, 198519 citations

On the theory of long-range spin-glass models

Hans-Jürgen Sommers

Journal of Magnetism and Magnetic MaterialsSep 1, 19796 citations

We discuss the zero-temperature behavior of the transverse Ising spin-glass ($\ifmmode\pm\else\textpm\fi{}{J}_{0}$) model. The

d

-dimensional quantum model is shown to be equivalent to a classical (

d+1

)-dimensional Ising spin glass with correlated disorder. A renormalization-group treatment of the one-dimensional quantum model indicates the existence of a spin-glass phase. The Migdal-Kadanoff approximation is used to obtain the phase diagram of the quantum spin glass in two dimensions.